Finite Group Databasebeta

← C2×C3×D120 #13088000

Subgroups — C2×C3×D120 #13088000

Order 1440.

326 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D60C212yesmaximal, complemented
2C2×C32×C5×C8C211yesmaximal, characteristic, complemented
3C3×D120C214yesmaximal, direct product factor
4C2×D120C311yesmaximal, characteristic, direct product factor
5C2×C3×D40—31nomaximal
6C22×C3×D15—22no—
7C2×C32×C4×C5C2211yescharacteristic
8C3×D60—22no—
9C3×D60C2214yescomplemented
10C32×C5×C8C2212yescomplemented
11C2×C3×D24—51nomaximal, Hall
12C2×D60C2×C312yescomplemented
13C2×C3×D20—32no—
14C2×C3×C5×C8—21no—
15C2×C3×C5×C8D311yescharacteristic, complemented
16C2×C3×C5×C8C2×C311yescharacteristic, complemented
17D120C2×C314yesdirect product factor
18C3×D40—34no—
19C22×C32×C5D411yescharacteristic
20C2×C3×D15—24no—
21C2×C3×D15—44no—
22C32×C4×C5D411yescharacteristic
23C32×C4×C5C2311yescharacteristic
24C2×D40—31noHall
25C2×C3×D12—52no—
26C2×C32×C8D511yescharacteristic, complemented
27C3×D24—54no—
28C22×D15—22no—
29C22×C3×D5—62no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2×D311yescharacteristic
32C2×C3×C4×C5C22×C311yescharacteristic
33D60—22no—
34D60C22×C314yescomplemented
35C3×D20—34no—
36C3×D20—62no—
37C3×C5×C8—22no—
38C3×C5×C8C2×D312yescomplemented
39C3×C5×C8C22×C312yescomplemented
40C2×C3×D8—151no—
41C2×D24—51no—
42C2×C32×C5D812yescomplemented
43C2×C32×C5C2×D411yescharacteristic
44C3×D15—44no—
45C2×D20—32no—
46C2×C5×C8C3×D311yescharacteristic, complemented
47D40—34no—
48C22×C3×D3—102no—
49C2×C32×C4C2×D511yescharacteristic
50C3×D12—54no—
51C3×D12—102no—
52C32×C8C2×D512yescomplemented
53C22×C3×C5—21no—
54C22×C3×C5D1211yescharacteristic
55C22×C3×C5C3×D411yescharacteristic
56C2×D15—24no—
57C2×D15—44no—
58C2×C3×D5—64no—
59C2×C3×D5—124no—
60C3×C4×C5—21no—
61C3×C4×C5—21no—
62C3×C4×C5D1211yescharacteristic
63C3×C4×C5C3×D411yescharacteristic
64C3×C4×C5C22×D311yescharacteristic
65C3×C4×C5C23×C311yescharacteristic
66C2×C3×D4—152no—
67C2×D12—52no—
68C3×D8—154no—
69C2×C3×C8—21no—
70C2×C3×C8C3×D511yescharacteristic, complemented
71C2×C3×C8D1511yescharacteristic, complemented
72D24—54no—
73C32×C5C2×D811yescharacteristic, complemented, Hall
74C22×D5—62no—
75C2×C4×C5C2×C3×D311yescharacteristic
76D20—34no—
77D20—62no—
78C5×C8C2×C3×D312yescomplemented
79C22×C32D2011yescharacteristic
80C2×C3×D3—104no—
81C2×C3×D3—204no—
82C32×C4D2011yescharacteristic
83C32×C4C22×D511yescharacteristic
84C2×D8—151noSylow
85C2×C3×C5—22no—
86C2×C3×C5—21no—
87C2×C3×C5D2412yescomplemented
88C2×C3×C5C3×D812yescomplemented
89C2×C3×C5C2×D1211yescharacteristic
90C2×C3×C5C2×C3×D411yescharacteristic
91D15—44no—
92C3×D5—124no—
93C23×C3—302no—
94C22×D3—102no—
95C3×D4—154no—
96C3×D4—302no—
97C2×C3×C4—21no—
98C2×C3×C4C2×C3×D511yescharacteristic
99C2×C3×C4C2×D1511yescharacteristic
100D12—54no—
101D12—102no—
102C3×C8—22no—
103C3×C8C2×C3×D512yescomplemented
104C3×C8C2×D1512yescomplemented
105C22×C5C3×D1211yescharacteristic
106C2×D5—64no—
107C2×D5—124no—
108C4×C5C3×D1211yescharacteristic
109C4×C5C22×C3×D311yescharacteristic
110C2×C32D4012yescomplemented
111C2×C32C2×D2011yescharacteristic
112C3×D3—204no—
113C2×D4—152no—
114D8—154no—
115C2×C8C3×D1511yescharacteristic, complemented
116C3×C5—21no—
117C3×C5C2×D2411yescharacteristic, complemented
118C3×C5C2×C3×D811yescharacteristic, complemented
119C22×C3—21no—
120C22×C3—304no—
121C22×C3—604no—
122C22×C3C3×D2011yescharacteristic
123C22×C3D6011yescharacteristic
124C2×D3—104no—
125C2×D3—204no—
126C3×C4—21no—
127C3×C4—21no—
128C3×C4C3×D2011yescharacteristic
129C3×C4D6011yescharacteristic
130C3×C4C22×C3×D511yescharacteristic
131C3×C4C22×D1511yescharacteristic
132C2×C5C3×D2412yescomplemented
133C2×C5C2×C3×D1211yescharacteristic
134D5—124no—
135C32C2×D4011yescharacteristic, complemented, Sylow
136C23—302no—
137D4—154no—
138D4—302no—
139C2×C4C2×C3×D1511yescharacteristic
140C8C2×C3×D1512yescomplemented
141C2×C3—21no—
142C2×C3—22no—
143C2×C3—604no—
144C2×C3C3×D4012yescomplemented
145C2×C3D12012yesdirect product factor
146C2×C3C2×C3×D2011yescharacteristic
147C2×C3C2×D6011yescharacteristic
148D3—204no—
149C5C2×C3×D2411yescharacteristic, complemented, Sylow
150C22—304no—
151C22—604no—
152C22C3×D6011yescharacteristic
153C4C3×D6011yescharacteristic
154C4C22×C3×D1511yescharacteristic
155C3—21no—
156C3C2×C3×D4011yescharacteristic, complemented
157C3C2×D12011yescharacteristic, direct product factor
158C2—604no—
159C2C3×D12012yesdirect product factor
160C2C2×C3×D6011yescharacteristic
subgroupG/H
centerC22×C3D60
commutator, cosocleC3×C4×C5C23×C3
FrattiniC4C22×C3×D15
FittingC2×C32×C5×C8C2
socleC22×C32×C5D4
hypercenterC2×C3×C8D15
hypocenterC3×C5C2×C3×D8
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×D60C2semidirect
2. C2×C32×C5×C8C2semidirect
3. C3×D120C2direct (N × H)
4. C2×D120C3direct (N × H)
9. C3×D60C22semidirect
10. C32×C5×C8C22semidirect
12. C2×D60C2×C3semidirect
15. C2×C3×C5×C8D3semidirect
16. C2×C3×C5×C8C2×C3semidirect
17. D120C2×C3direct (N × H)
26. C2×C32×C8D5semidirect
34. D60C22×C3semidirect
38. C3×C5×C8C2×D3semidirect
39. C3×C5×C8C22×C3semidirect
42. C2×C32×C5D8semidirect
46. C2×C5×C8C3×D3semidirect
52. C32×C8C2×D5semidirect
70. C2×C3×C8C3×D5semidirect
71. C2×C3×C8D15semidirect
73. C32×C5C2×D8semidirect
78. C5×C8C2×C3×D3semidirect
87. C2×C3×C5D24semidirect
88. C2×C3×C5C3×D8semidirect
103. C3×C8C2×C3×D5semidirect
104. C3×C8C2×D15semidirect
110. C2×C32D40semidirect
115. C2×C8C3×D15semidirect
117. C3×C5C2×D24semidirect
118. C3×C5C2×C3×D8semidirect
132. C2×C5C3×D24semidirect
135. C32C2×D40semidirect
140. C8C2×C3×D15semidirect
144. C2×C3C3×D40semidirect
145. C2×C3D120direct (N × H)
149. C5C2×C3×D24semidirect
156. C3C2×C3×D40semidirect
157. C3C2×D120direct (N × H)
159. C2C3×D120direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×D602
C2×C32×C5×C82
C3×D1202
C2×D1203
C2×C3×D403
C2×C3×D245